Bernoulli
- Bernoulli
- Volume 7, Number 3 (2001), 381-420.
Asymptotics of the maximum likelihood estimator for general hidden Markov models
Randal Douc and Catherine Matias
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Abstract
In this paper, we consider the consistency and asymptotic normality of the maximum likelihood estimator for a possibly non-stationary hidden Markov model where the hidden state space is a separable and compact space not necessarily finite, and both the transition kernel of the hidden chain and the conditional distribution of the observations depend on a parameter θ. For identifiable models, consistency and asymptotic normality of the maximum likelihood estimator are shown to follow from exponential memorylessness properties of the state prediction filter and geometric ergodicity of suitably extended Markov chains.
Article information
Source
Bernoulli Volume 7, Number 3 (2001), 381-420.
Dates
First available in Project Euclid: 22 March 2004
Permanent link to this document
http://projecteuclid.org/euclid.bj/1080004757
Mathematical Reviews number (MathSciNet)
MR2002e:62081
Zentralblatt MATH identifier
0987.62018
Keywords
asymptotic normality consistency geometric ergodicity hidden Markov models identifiability maximum likelihood estimation
Citation
Douc, Randal; Matias, Catherine. Asymptotics of the maximum likelihood estimator for general hidden Markov models. Bernoulli 7 (2001), no. 3, 381--420. http://projecteuclid.org/euclid.bj/1080004757.
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